***question*******
Is (1) correct? I am confused because as the provided information
Yn n=1..M are discrete random variables which are conditionally independent
given X. That means P(Y(0),...Y(N)|X)=P(Y(0)|X)*...P(Y(N)|X)
where X is a whole chain, not only one sample X(n).
Does it still guarantee P(Y(0),...Y(N)|X(N))=P(Y(0)|X(N))*...P(Y(N)|X(N))? ?